Starts 2 Jul 2024 11:00
Ends 2 Jul 2024 12:00
Central European Time
CMSP Seminar (Joint ICTP/SISSA Statistical Physics): Minors or: how I learned to stop worrying and love the exponential
Leonardo Building, Luigi Stasi Seminar Room
M. Ali Rajabpour
(Uni. Federal Fluminense Instituto de Fisica, Brazil)
Abstract:
The Sum of Powers of Principal Minors (SPPM) of matrices is used in calculating the Rényi entropy in fermionic systems, the partition function of the Hubbard model, and the partition function of weighted rooted spanning forests when the matrix in question is the graph's Laplacian. It is likely that no polynomial-time solution exists to estimate SPPM. Initially, I will discuss how the Rényi (Shannon) entropy in quantum chains can identify different phases and classify universality classes. The core of this talk will introduce a Grassmann representation for a generic matrix SPPM problem. Leveraging this representation, I will outline three distinct yet compatible mean-field approximations, providing an accurate estimation of the Rényi entropy for the Ising chain. Lastly, I will discuss how the SPPM problem can be viewed as the partition function for rooted spanning forests and use the cavity method (belief propagation) to calculate it.